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Cross-validation techniques for risk estimation and model selection arewidely used in statistics and machine learning. However, the understanding ofthe theoretical properties of learning via model selection withcross-validation risk estimation is quite low in face of its widespread use. Inthis context, this paper presents learning via model selection withcross-validation risk estimation as a general systematic learning frameworkwithin classical statistical learning theory and establishes distribution-freedeviation bounds in terms of VC dimension, giving detailed proofs of theresults and considering both bounded and unbounded loss functions. We alsodeduce conditions under which the deviation bounds of learning via modelselection are tighter than that of learning via empirical risk minimization inthe whole hypotheses space, supporting the better performance of modelselection frameworks observed empirically in some instances.

Distribution-free Deviation Bounds of Learning via Model Selection with Cross-validation Risk Estimation